Question

Find the inverse of the matrix $\left(\begin{array}{l l }-3 & 2 \\ 5 & -3\end{array}\right)$ Hence, find the matrix P satisfying the matrix equation P$\left(\begin{array}{l l }-3 & 2 \\ 5 & -3\end{array}\right)$ = $\left(\begin{array}{l l }1 & 2 \\ 2 & -1\end{array}\right)$ .

If A = $\begin{vmatrix}2 & 3 & -1 \\ 4 & 1 & 0 \\ 3 & 3 & 2\end{vmatrix}$ , find $M_{12}\times M_{21}+C_{21}\times C_{12}$ when $M_{i j}$ is called minor and $C_{i j}$ is called co-factors of A.

Find : $\textstyle\int$${\frac{\left(x^{4}-x\right)^{\frac{1}{4}}}{x^{5}}}\,.$

The volume of a cube is increasing at the rate of 9 cm³/sec. How fast is the surface area increasing when the length of an edge is 10 cm.

From the differential equation of equation y = a cos 2x + b sin 2x, where a and b are constant.

Find : $\textstyle\int$$\frac{d x}{\sqrt{3-2\,x-x^{2}}}$

If A and B are square matrices of order 3 such that |A| = –1, |B| = 3, then find the value of |2AB|.